Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T17:47:33.242Z Has data issue: false hasContentIssue false
  • English
  • Français

IDENTIFYING MULTIPLE MARGINAL EFFECTS WITH A SINGLE INSTRUMENT

Published online by Cambridge University Press:  19 May 2020

Carolina Caetano  and
Juan Carlos Escanciano
Carolina Caetano*
Affiliation:
University of Georgia
Juan Carlos Escanciano
Affiliation:
Universidad Carlos III de Madrid
*
Address correspondence to Carolina Caetano, Department of Economics, University of Georgia, 620 South Lumpkin Street Athens, GA30602, USA; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a new strategy for the identification of the marginal effects of an endogenous multivalued variable (which can be continuous, or a vector) in a model with an Instrumental Variable (IV) of lower dimension, which may even be a single binary variable, and multiple controls. Despite the failure of the classical order condition, we show that identification may be achieved by exploiting heterogeneity of the “first stage” in the controls through a new rank condition that we term covariance completeness. The identification strategy justifies the use of interactions between instruments and controls as additional exogenous variables and can be straightforwardly implemented by parametric, semiparametric, and nonparametric two-stage least squares estimators, following the same generic algorithm. Monte Carlo simulations show that the estimators have excellent performance in moderate sample sizes. Finally, we apply our methods to the problem of estimating the effect of air quality on house prices, based on Chay and Greenstone (2005, Journal of Political Economy 113, 376–424). All methods are implemented in a companion Stata software package.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 3 , June 2021 , pp. 464 - 494
Copyright
© Cambridge University Press 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

We would like to thank Gregorio Caetano, Alon Bergman, Kenneth Chay, Matias Cattaneo, Pedro Sant’Anna, and and Robin Sickles for helpful discussions. We are thankful to the Co-Editor and three referees for suggestions, which have helped us to significantly improve the presentation. We would also like to thank seminar participants at many institutions as well as guests at our institutions for useful comments. This paper subsumes part of the working paper “Identifying Multiple Marginal Effects with a Single Binary Instrument or by Regression Discontinuity,” dated May 25, 2015. Research funded to Juan Carlos Escanciano by the Spanish Grant PGC2018-096732-B-I00.

References

Ai, C. & Chen, X. (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71(6), 1795–1843.CrossRefGoogle Scholar
Almond, D. & Currie, J. (2011) Killing me softly: The fetal origins hypothesis. The Journal of Economic Perspectives 25(3), 153–172.CrossRefGoogle ScholarPubMed
Altonji, J.G. & Matzkin, R.L. (2005) Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica 73, 1053–1102.CrossRefGoogle Scholar
Andrews, D. (2017) Examples of L2-complete and boundedly-complete distributions. Journal of Econometrics 199, 213–220.CrossRefGoogle Scholar
Ben-Moshe, D., D’Haultfoeuille, X. & Lewbel, A. (2017) Identification of additive and polynomial models of mismeasured regressors without instruments. Journal of Econometrics 200, 207–222.CrossRefGoogle Scholar
Blundell, R., Chen, X. & Kristensen, D. (2007) Semi-nonparametric IV estimation of shape-invariant Engel curves Econometrica 75, 1613–1670.CrossRefGoogle Scholar
Caetano, C., Escanciano, J.C. & Bergman, A. (2019) MMEIV: Stata module to perform Multiple Marginal Effects IV Estimation. Statistical Software Components S458674, Boston College Department of Economics.Google Scholar
Card, D. (2001) Estimating the return to schooling: Progress on some persistent econometric problems. Econometrica 69, 1127–1160.CrossRefGoogle Scholar
Chay, K. & Greenstone, M. (2005) Does air quality matter? Evidence from the housing market. Journal of Political Economy 113(2), 376–424.CrossRefGoogle Scholar
Chen, X. & Christensen, T. (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression. Quantitative Economics 9(1), 39–84.CrossRefGoogle Scholar
Chen, X. & Pouzo, D. (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals. Econometrica 80(1), 277–321.Google Scholar
Chen, X. & Pouzo, D. (2015) Sieve Wald and QLR inference on semi/nonparametric conditional moment models. Econometrica 83(3), 1013–1079.CrossRefGoogle Scholar
Chernozhukov, V. & Hansen, C. (2005) An IV model of quantile treatment effects. Econometrica 73, 245–261.CrossRefGoogle Scholar
Chesher, A. (2003) Identification in nonseparable models. Econometrica 71, 1405–1441.CrossRefGoogle Scholar
D’Haultfoeuille, X. (2011) On the completeness condition in nonparametric instrumental problems. Econometric Theory 1, 1–12.Google Scholar
D’Haultfoeuille, X. & Fevrier, P. (2015) Identification of nonseparable models with endogeneity and discrete instruments. Econometrica 83, 1199–1210.CrossRefGoogle Scholar
D’Haultfoeuille, X., Holderlein, S. & Sasaki, Y. (2013) Nonlinear Difference-in-Differences in Repeated Cross Sections with Continuous Treatments, Boston College Working Paper wp839.CrossRefGoogle Scholar
Darolles, S., Fan, Y., Florens, J.P. & Renault, E. (2011) Nonparametric instrumental regression. Econometrica 79(5), 1541–1565.Google Scholar
Dunker, F., Florens, J.-P., Hohage, T., Johannes, J. & Mammen, E. (2014) Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression. Journal of Econometrics 178, 444–455.CrossRefGoogle Scholar
Florens, J.P., Heckman, J.J., Meghir, C. & Vytlacil, E. (2008) Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effect. Econometrica 76, 1191–1207.Google Scholar
Frolich, M. (2008) Parametric and nonparametric regression in the presence of endogenous control variables. International Statistical Review 76, 214–227.CrossRefGoogle Scholar
Horowitz, J. (2011) Applied nonparametric instrumental variables estimation. Econometrica 79(2), 347–394.Google Scholar
Horowitz, J. (2014) Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter. Journal of Econometrics 180, 158–173.CrossRefGoogle Scholar
Huang, L., Khalil, U. & Yildiz, N. (2019) Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables. Journal of Econometrics 208, 346–366.CrossRefGoogle Scholar
Kim, K.I. & Song, S. (2017) Estimation of Semiparametric Models with Mismeasured Endogenous Regressors Using Control Variables. Working Paper.Google Scholar
Lumley, J., Chamberlain, C., Dowswell, T., Oliver, S., Oakley, L. & Watson, L. (2009) Interventions for promoting smoking cessation during pregnancy (Cochrane Review). The Cochrane Library 8, 3.Google Scholar
Masten, M. & Torgovitsky, A. (2016) Identification of instrumental variable correlated random coefficients models. The Review of Economics and Statistics 98(5), 1001–1005.CrossRefGoogle Scholar
Matzkin, R.L. (2013) Nonparametric identification in structural economic models. Annual Review of Economics 5, 457.CrossRefGoogle Scholar
Newey, W.K. & Powell, J. (2003) Instrumental variables estimation for nonparametric models. Econometrica 71, 1565–1578.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2011) Introduction to Econometrics, 3rd ed. Addison Wesley.Google Scholar
Torgovitsky, A. (2015) Identification of nonseparable models using instruments with small support. Econometrica 83, 1185–1197.CrossRefGoogle Scholar
Wahba, G. (1990) Spline Models for Observational Data. SIAM.CrossRefGoogle Scholar